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arXiv:2602.14036

Enhancing collective spin squeezing via one-axis twisting echo control of individual atoms

Zhiwei Hu, Youwei Zhang, Junlei Duan, Mingfeng Wang, Yanhong Xiao

quant-phSubmitted Feb 15, 2026• Announced Feb 17, 2026• 0 citations
v1 · Feb 15, 2026v2 · May 15, 2026
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Abstract

Spin squeezing generated via inter-atom entanglement in multilevel atomic ensembles provides a powerful resource for quantum-enhanced metrology. Existing schemes that harness internal atomic degrees of freedom to boost squeezing typically encode the collective squeezing in complex superpositions of magnetic sublevels, which complicates state control and limits practical applications. Here, we propose a coherent control scheme that simultaneously enhances collective spin squeezing and maps the resulting atom-atom entanglement onto two well-defined magnetic sublevels suitable for subsequent metrology experiments. Our protocol sandwiches a quantum non-demolition measurement between two internal one-axis-twisting interactions arranged in an echo sequence. We show that this approach can optimally leverage internal states to boost the inter-atom entanglement and, at the same time, encode it in two magnetic sublevels, which is readily convertible into metrologically useful spin squeezing. Our results offer a straightforward and efficient strategy for generating highly entangled yet readily accessible quantum states in multilevel atomic systems.

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6pages, 2figures

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Spin squeezing generated via inter-atom entanglement in multilevel atomic ensembles provides a powerful resource for quantum-enhanced metrology. Existing schemes that harness internal atomic degrees of freedom to boost squeezing typically encode the collective squeezing in complex superpositions of magnetic sublevels, which complicates state control and limits practical applications. Here, we propose a coherent control scheme that simultaneously enhances collective spin squeezing and maps the resulting atom-atom entanglement onto two well-defined magnetic sublevels suitable for subsequent metrology experiments. Our protocol sandwiches a quantum non-demolition measurement between two internal one-axis-twisting interactions arranged in an echo sequence. We show that this approach can optimally leverage internal states to boost the inter-atom entanglement and, at the same time, encode it in two magnetic sublevels, which is readily convertible into metrologically useful spin squeezing. Our results offer a straightforward and efficient strategy for generating highly entangled yet readily accessible quantum states in multilevel atomic systems.
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The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to SU(2)\text{SU}(2)SU(2) rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in SU(4)\text{SU}(4)SU(4), thereby creating the opportunity for dynamics not possible in typical SU(2)\text{SU}(2)SU(2) one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.
Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.
Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field or by state-dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so that atoms behave like pseudospin-12\frac{1}{2}21​ particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of 106{10}^{6}106 Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of at least 5dB is generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise allows us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Our work sets the stage for experiments on quantum feedback, deterministic squeezing, and closed-loop magnetometry. The implementation of real-time feedback may also create an opportunity for new types of quantum simulation, wherein the evolution of a quantum system is conditioned on the outcome of a time-continuous QND measurement. Such a scheme has the potential to access new regimes near the quantum-classical boundary, with opportunities to study long-standing issues related to quantum-classical correspondence in chaotic systems.